aiqbench analysis
This study provides a theoretical framework for generative models under finite training sets, deriving closed-form expressions for velocity fields and score functions that clarify how stochastic processes manifest as training samples with added Gaussian noise. The analysis formally defines underfitting and overfitting within this specific generative context, showing that estimation errors result in convex combinations of samples corrupted by mixed uniform and Gaussian noise. Experimental validation on generation and classification tasks supports these findings, offering a rigorous basis for understanding model behavior when training data is limited.
Generation Properties of Stochastic Interpolation under Finite Training Set
arXiv:2509.21925v2 Announce Type: replace Abstract: This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score function when only a finite number of training samples are available. We demonstrate that, under some regularity conditions, the deterministic generative process exactly recovers the training samples, while the stochastic generative process manifests as training samples with added Gaussian noise. Beyond the idealized setting, we consider model estimation errors and introduce formal definitions of underfitting and overfitting specific to generative models. Our theoretical analysis reveals that, in the presence of estimation errors, the stochastic generation process effectively produces convex combinations of training samples corrupted by a mixture of uniform and Gaussian noise. Experiments on generation tasks and downstream tasks such as classification support our theory.
Abstract:This paper investigates the theoretical behavior of generative models under finite training populations. Within the stochastic interpolation generative framework, we derive closed-form expressions for the optimal velocity field and score function when only a finite number of training samples are available. We demonstrate that, under some regularity conditions, the deterministic generative process exactly recovers the training samples, while the stochastic generative process manifests as training samples with added Gaussian noise. Beyond the idealized setting, we consider model estimation errors and introduce formal definitions of underfitting and overfitting specific to generative models. Our theoretical analysis reveals that, in the presence of estimation errors, the stochastic generation process effectively produces convex combinations of training samples corrupted by a mixture of uniform and Gaussian noise. Experiments on generation tasks and downstream tasks such as classification support our theory.
We found errors in the proof and added some new theorems. We have reorganized the logic of the paper and intend to submit it as a new paper
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2509.21925 [cs.LG]
(or arXiv:2509.21925v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2509.21925 Focus to learn more arXiv-issued DOI via DataCite
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